Year: 2026
Type: preprint
Abstract: On a connected compact Riemannian spin manifold with boundary, we prove an upper estimate for the smallest eigenvalue of the Dirac operator under the boundary condition associated with a chirality operator. This upper bound is expressed in terms of the hyper-hemispherical radius. Moreover, the upper bound is realized if and only if the manifold is a hemisphere. As an application, we get a scalar curvature rigidity result for the hemisphere in the case of Lipschitz maps whose differential has a prescribed trace-norm bound. Our estimate extends Bär's result for closed manifolds, where the upper bound is given in terms of hyperspherical radius.
Source: arXiv (Cornell University)
Author: Shi, Pengshuai
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223708738